In this topic, we consider the Kelvin transform for Laplaction operators. Precisely, what we get is the following
.
We now consider a different situation. The detail can be found in the following paper due to X.W. Xu published in Proc. Roy. Soc. Edinburgh Sect. A, 2000.
Theorem. If
is a sufficiently good function then
satisfies the equation
where
is defined to be
.